Last time I gave you a piece of my mind when it comes to the Kuratowski definition of pairs and ordered sets, and why we should stay away from it in linguistics. The thing is, that was a conceptual argument, and those tend to fall flat with most researchers. Just like most mathematicians weren’t particularly fazed by Gödel’s incompleteness results because it didn’t impact their daily work, the average researcher doesn’t care about some impurities in their approach as long as it gets the job done. So this post will discuss a concrete case where a good linguistic insight got buried under mathematical rubble.

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As some of you might know, my dissertation starts with a quote from My Little Pony. By Applejack, to be precise, the only pony that I could see myself have a beer with (and I don’t even like beer). You can watch the full clip, but here’s the line that I quoted:

Don’t you use your fancy mathematics to muddy the issue.

Truer words have never been spoken. In light of my obvious mathematical inclinations this might come as a surprise for some of you, but I don’t like using math just for the sake of math. Mathematical formalization is only worth it if it provides novel insights.

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Bill Idsardi brought this to my attention. Enjoy your reading!

Star-Free Regular Languages and Logic

on the Gödel’s Lost Letter and P=NP blog.

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Here’s another quick follow-up to the unboundedness argument. As you might recall, that post discussed a very simple model of syntax whose only task it was to adjudicate the well-formedness of a small number of strings. Even for such a limited task, and with such a simple model, it quickly became clear that we need a more modular approach to succinctly capture the facts and state important generalizations. But once we had this more modular perspective, it no longer mattered whether syntax is actually unbounded. Assuming unboundedness, denying unboundedness, it doesn’t matter because the overall nature of the approach does not hinge on whether we incorporate an upper bound on anything. Well, something very similar also happens with another aspect of syntax that is beyond doubt in some communities and highly contentious in others: syntactic trees.

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Ignas Rudaitis left a comment under my unboundedness post that touches on an important issue: the interaction of unboundedness and the poverty of the stimulus (POS). My reply there had to be on the short side, so I figured I’d fill in the gaps with a short follow-up post.

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Jon’s post on the overappreciated Marr argument reminded me that it’s been a while since the last entry in the Underappreciated arguments series. And seeing how the competence-performance distinction showed up in the comments section of my post about why semantics should be like parsing, this might be a good time to talk one of the central tenets of this distinction: unboundedness. Unboundedness, and the corollary that natural languages are infinite, is one of the first things that we teach students in a linguistics intro, and it is one of the first things that psychologists and other non-linguists will object to. But the dirty secret is that nothing really hinges on it.

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Last week I blogged a bit about syntax textbooks. One question I didn’t ask there, for fear of completely derailing the post, is what should actually be in a syntax textbook. There’s a common complaint I hear from students about syntax classes, and it’s that syntax courses are one giant bait-and-switch. They’re right, and it’s also true for syntax textbooks.

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Recently I found in my inbox an inquiry from a student who wants to pick up syntax on their own and would like to get some textbook recommendations. I happily complied, but I’m actually not all that qualified to give such recommendations. It’s been a long time since I’ve read a syntax textbook. I have never taught a grad-level syntax introduction. At the undergraduate level I got to teach syntax twice at the very beginning of my Stony Brook career, and never again since then — I can only surmise that what I did in those courses was too radical for the linguistic deep state to tolerate. But the prestigious Outdex readership includes at least some syntacticians, so why not crowdsource the recommendations?

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Congratulations, you’re reading the shortest Outdex post yet! Peter Woit of Not Even Wrong, reacting to Sabine Hossenfelder of Lost in Math fame, has another post on the lack of progress in high-energy particle physics. If you’ve been following the debate about string theory and super symmetry in recent years, nothing in the post will shock you. What I find fascinating is that you could replace “particle physics” by “Minimalism” in this debate and the whole thing all of a sudden looks very familiar.

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<TG soapbox> The following is a guest post by Jon Rawski. I’m ruthlessly abusing my editorial powers to insert this reminder that the Outdex welcomes guest posts. Maybe you’d like to start a discussion on a topic that’s dear to your heart? Or maybe you have something to add to an ongoing discussion that can’t be fit in the comments section because it’s too long and involves multiple pictures and figures? Just send me your post in some editable format (not PDF) and I’ll try to post it asap. If you want to reduce the time from sending to posting, check the instructions on how to reduce the editorial load for me. Anyways, enough of my blabbering, let’s hear what Jon has to say… <TG soapbox/>

To spice up the Underappreciated Arguments series, I thought I’d describe a rhetorical chestnut beloved by many a linguist: Marr’s Three Levels. Anyone who has taken a linguistics class that dips a toe into the cognitive pool has heard of the Three Levels argument. It’s so ubiquitous that it’s been memed by grad students.

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